2048 expectimax python

The "min" part means that you try to play conservatively so that there are no awful moves that you could get unlucky. Scoring is also done using table lookup. 2048 Python game and AI 27 Sep 2015. If it isnt over yet, we add a new row to our matrix using add_new_2(). def cover_left (matrix): new= [ [0,0,0,0], [0,0,0,0], [0,0,0,0], [0,0,0,0]] for i . While Minimax assumes that the adversary(the minimizer) plays optimally, the Expectimax doesnt. To assess the score performance of the AI, I ran the AI 100 times (connected to the browser game via remote control). Mixed Layer Types E.g. Backgammon Expectiminimax Environment is an extra player that moves after each agent Chance nodes take expectations, otherwise like minimax. (PSO) algorithm in Python which includes a basic model along with few advanced features such as updating inertia weight, cognitive, social learning coefficients and . For example, 4 is a moderate speed, decent accuracy search to start at. I developed a 2048 AI using expectimax optimization, instead of the minimax search used by @ovolve's algorithm. While Minimax assumes that the adversary (the minimizer) plays optimally, the Expectimax doesn't. This is useful for modelling environments where adversary agents are not optimal, or their actions are . Next, we have a function to initialize the matrix. The game contrl part code are used from 2048-ai. The code first creates a boolean variable, changed, to indicate whether the new grid after merging is different. If the search depth is limited to 6 moves, the AI can easily execute 20+ moves per second, which makes for some interesting watching. 2048 game solved with Expectimax. This is the first article from a 3-part sequence. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Following the above process we have to double the elements by adding up and make 2048 in any of the cell. I'm the author of the AI program that others have mentioned in this thread. The result it reaches when starting with an empty grid and solving at depth 5 is: Source code can be found here: https://github.com/popovitsj/2048-haskell. the entire board filled with 4 .. 65536 each once - 15 fields occupied) and the board has to be set up at that moment so that you actually can combine. Variance of the board game Settlers of Catan, with a University/Campus theme, Solutions to Pacman AI Multi-Agent Search problems. game.exe -a Expectimax. This is done by appending an empty list to each row and then referencing the individual list items within that row. Expectimax is not optimal. By using our site, you The latest version of 2048-Expectimax is current. I am an aspiring developer with experience in building web-based application, have a good understanding of python language and a competitive programmer with passion for learning and solving challenging problems. Then the average end score per starting move is calculated. Specify a number for the search tree depth. Here we evaluate faces that have the possibility to getting to merge, by evaluating them backwardly, tile 2 become of value 2048, while tile 2048 is evaluated 2. A Connect Four game which can be played by an AI: uses alpha beta pruning algorithm when played against a human and expectimax algorithm when played against a random player. The code first declares a variable i to represent the row number and j to represent the column number. Most of the times it either stops at 1024 or 512. Python: Justifying NumPy array. x]7r}QiuUWe,QVbc!gvMvSM$c->(P%w$( _B}x2oFauV,nY-] Next, it updates the grid matrix based on the inputted direction. Running 10000 runs with a temporary increase to 1000000 near critical positions managed to break this barrier less than 1% of the times achieving a max score of 129892 and the 8192 tile. If at any point during the loop, all four cells in mat have a value of 0, then the game is not over and the code will continue to loop through the remaining cells in mat. It's interesting to see the red line is just a tiny bit above the blue line at each point, yet the blue line continues to increase more and more. A tag already exists with the provided branch name. Pokmon battles simulator, with the use of MiniMax-Type algorithms (Artificial Intelligence project), UC Berkeley CS188 Intro to AI -- Pacman Project Solutions. The AI never failed to obtain the 2048 tile (so it never lost the game even once in 100 games); in fact, it achieved the 8192 tile at least once in every run! The game infrastructure is used code from 2048-python.. Implementation of Expectimax for an AI agent to play 2048. I think I have this chain or in some cases tree of dependancies internally when deciding my next move, particularly when stuck. If you order a special airline meal (e.g. Currently student at IIIT Gwalior. This version allows for up to 100000 runs per move and even 1000000 if you have the patience. This intuition will give you also the upper bound for a tile value: where n is the number of tile on the board. game.exe -h: usage: game.exe [-h] [-a AGENT] [-d DEPTH] [-g GOAL] [--no-graphics] 2048 Game w/ AI optional arguments: -h, --help show this help message and exit -a AGENT, --agent AGENT name of agent (Reflex or Expectimax) -d DEPTH . Just play 2048! <> The median score is 387222. A proper AI would try to avoid getting to a state where it can only move into one direction at all cost. 2 0 obj Finally, both original grids and transposed matrices are returned. The Chance nodes take the average of all available utilities giving us the expected utility. Larger tile in the way: Increase the value of a smaller surrounding tile. It could be this mechanical in feel lacking scores, weights, neurones and deep searches of possibilities. Currently, the program achieves about a 90% win rate running in javascript in the browser on my laptop given about 100 milliseconds of thinking time per move, so while not perfect (yet!) how the game board is modeled (as a graph), the optimization employed (min-max the difference between tiles) etc. In the beginning, we will build a heuristic table to save all the possible value in one row to speed up evaluation process. The while loop runs until the user presses any of the keyboard keys (W, S, A, D). If they are, then their values are set to be 2 times their original value and the next cell in that column is emptied so that it can hold a new value for future calculations. The starting move with the highest average end score is chosen as the next move. The AI simply performs maximization over all possible moves, followed by expectation over all possible tile spawns (weighted by the probability of the tiles, i.e. Connect and share knowledge within a single location that is structured and easy to search. The code compresses the grid after every step before and after merging cells. Also, I tried to increase the search depth cut-off from 3 to 5 (I can't increase it more since searching that space exceeds allowed time even with pruning) and added one more heuristic that looks at the values of adjacent tiles and gives more points if they are merge-able, but still I am not able to get 2048. to use Codespaces. The code compresses the grid by copying each cells value to a new list. Here's a demonstration of the power of this approach. Fast integer matrix multiplication with bit-twiddling hacks, Algorithm to find counterfeit coin amongst n coins. For each value, it generates a new list containing 4 elements ( [0] * 4 ). (In case of no legal move, the cycle algorithm just chooses the next one in clockwise order). The code first creates a boolean variable called changed and sets it equal to True. This heuristic alone captures the intuition that many others have mentioned, that higher valued tiles should be clustered in a corner. Try to extend it with the actual rules. Below animation shows the last few steps of the game played by the AI agent with the computer player: Any insights will be really very helpful, thanks in advance. By using our site, you Learn more. A tag already exists with the provided branch name. If both conditions are met, then the value of the current cell is doubled and set to 0 in the next cell in the row. Therefore we decided to develop an AI agent to solve the game. There is also a discussion on Hacker News about this algorithm that you may find useful. ExpectiMax. However randomization in Haskell is not that bad, you just need a way to pass around the `seed'. The code then moves the grid left using the move_left function. Currently porting to Cuda so the GPU does the work for even better speeds! Maximum points AFAIK is slightly more than 20,000 points which is way larger than my current score. You can view the AI in action or read the source. If any cell does, then the code will return WON. the board position and the player that is next to move). sophisticated decision rule will slow down the algorithm and it will require some time to be implemented.I will try a minimax implementation in the near future. The source files for the implementation can be found here. One, I need to follow a well-defined strategy to reach the goal. I'd be interested to hear if anyone has other improvement ideas that maintain the domain-independence of the AI. I developed a 2048 AI using expectimax optimization, instead of the minimax search used by @ovolve's algorithm. Please First I created a JavaScript version which can be seen in action here. I played with many possible weight assignments to the heuristic functions and take a convex combination, but very rarely the AI player is able to score 2048. 2048-Expectimax has no issues reported. Some little games implementation, and also, machine learning implementation. This is possible due to domain-independent nature of the AI. I uncapped the tile values (so it kept going after reaching 2048) and here is the best result after eight trials. This is not a direct answer to OP's question, this is more of the stuffs (experiments) I tried so far to solve the same problem and obtained some results and have some observations that I want to share, I am curious if we can have some further insights from this. The class is in src\Expectimax\ExpectedMax.py.. Finally, it adds these lists together to create new_mat . It is sensitive to monotonic transformations in utility values. Not sure why this doesn't have more upvotes. I also tried the corner heuristic, but for some reason it makes the results worse, any intuition why? How can I find the time complexity of an algorithm? The code inside this loop will be executed until user presses any other key or the game is over. Stochastic Two-Player We also need to call get_current_state() to get information about the current state of our matrix. If you recall from earlier in this chapter, these are references to variables that store data about our game board. Rest cells are empty. Next, the code loops through each column in turn. A tag already exists with the provided branch name. In here we still need to check for stacked values, but in a lesser way that doesn't interrupt the flexibility parameters, so we have the sum of { x in [4,44] }. Use Git or checkout with SVN using the web URL. The assumption on which my algorithm is based is rather simple: if you want to achieve higher score, the board must be kept as tidy as possible. Although, it has reached the score of 131040. We call the function recursively until we reach a terminal node(the state with no successors). The code will check each cell in the matrix (mat) and see if it contains a value of 2048. Implementation of reinforcement learning algorithms to solve pacman game. In theory it's alternating 2s and 4s. Are you sure you want to create this branch? Several heuristics are used to direct the optimization algorithm towards favorable positions. I have refined the algorithm and beaten the game! The whole approach will likely be more complicated than this but not much more complicated. The code starts by declaring two variables, r and c. These will hold the row and column numbers at which the new 2 will be inserted into the grid. Tool assisted superplay of 2048 game using Expectimax algorithm in Python.Chapters:0:00 TAS0:24 ExplanationReferences:https://2048game.com/https://en.wikiped. A rust implementation of the famous 2048 game. The Expectimax search algorithm is a game theory algorithm used to maximize the expected utility. ), https://github.com/yangshun/2048-python (gui), https://stackoverflow.com/questions/22342854/what-is-the-optimal-algorithm-for-the-game-2048 (using idea of smoothness referenced here in eval function), https://stackoverflow.com/questions/44580615/python-how-to-merge-equal-element-numpy-array (using merge with numba referenced here), https://stackoverflow.com/questions/44558215/python-justifying-numpy-array (ended up using numba for justify), http://techieme.in/matrix-rotation/ (transpose reverse transpose transpose .. cool diagrams). The actual score, as shown by the game, is not used to calculate the board score, since it is too heavily weighted in favor of merging tiles (when delayed merging could produce a large benefit). You signed in with another tab or window. The AI program was implemented with expectimax algorithm to solve puzzle and form 2048 tile. Surprisingly, increasing the number of runs does not drastically improve the game play. The first, mat, is an array of four integers. Updated on Aug 10, 2022. Solving 2048 using expectimax and Clojure. More spaces makes the state more flexible, we multiply by 128 (which is the median) since a grid filled with 128 faces is an optimal impossible state. But if during the game there is no empty cell left to be filled with a new 2, then the game goes over. Otherwise, we break out of the loop because theres nothing else left to do in this code block! Finally, it transposes the newly created grid to return it to its original form. Either do it explicitly, or with the Random monad. Just plays it randomly once. stream (This is the link of my blog post for the article: https://sandipanweb.wordpress.com/2017/03/06/using-minimax-with-alpha-beta-pruning-and-heuristic-evaluation-to-solve-2048-game-with-computer/ and the youtube video: https://www.youtube.com/watch?v=VnVFilfZ0r4). You can try the AI for yourself. The new_mat variable will hold the compressed matrix after it has been shifted to the left by one row and then multiplied by 2. The algorithm went from achieving the 16384 tile around 13% of the time to achieving it over 90% of the time, and the algorithm began to achieve 32768 over 1/3 of the time (whereas the old heuristics never once produced a 32768 tile). For a machine that has g++ installed, getting this running is as easy as. The first step of compression is to reduce the size of each row and column by removing any duplicate values. Using 10000 runs gets the 2048 tile 100%, 70% for 4096 tile, and about 1% for the 8192 tile. It performs pretty quickly for depth 1-4, but on depth 5 it gets rather slow at a around 1 second per move. Moving down can be done by taking transpose the moving right. The implementation of the AI described in this article can be found here. The first list (mat[0] ) represents cell 0 , and so on. The code first checks to see if the user has moved their finger (or swipe) right or left. INTRODUCTION 2048 is an stochastic puzzle game developed by Gabriele Cirulli[1]. Work fast with our official CLI. Could you update those? As far as I'm aware, it is not possible to prune expectimax optimization (except to remove branches that are exceedingly unlikely), and so the algorithm used is a carefully optimized brute force search. The 2048 game is a single-player game. It will typically prevent smaller valued tiles from getting orphaned and will keep the board very organized, with smaller tiles cascading in and filling up into the larger tiles. Discussion on this question's legitimacy can be found on meta: @RobL: 2's appear 90% of the time; 4's appear 10% of the time. Hello. But what if there is a possibility of the minimizer making a mistake(or not playing optimally). The code starts by importing the logic module. Play as single player and see what the heuristics do, or run with an AI at multiple search tree depths and see the highest score it can get. However, I have never observed it obtaining the 65536 tile. Work fast with our official CLI. The levels of the tree . My goal was to develop an AI that plays the game more similarly to how I've . How did Dominion legally obtain text messages from Fox News hosts? 1. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. 2048 is a very popular online game. It was submitted early in the response timeline. Please Expectimax requires the full search tree to be explored. There is already an AI implementation for this game here. Finally, it returns the new matrix and bool changed. @nneonneo I ported your code with emscripten to javascript, and it works quite well. The training method is described in the paper. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. There are 2 watchers for this library. Finally, it returns the updated grid and changed values. So it will press right, then right again, then (right or top depending on where the 4 has created) then will proceed to complete the chain until it gets: Second pointer, it has had bad luck and its main spot has been taken. The tables contain heuristic scores computed on all possible rows/columns, and the resultant score for a board is simply the sum of the table values across each row and column. 4 0 obj xkcdxkcd Therefore going right might sound more appealing or may result in a better solution. If nothing happens, download Xcode and try again. If nothing happens, download Xcode and try again. Theoretical limit in a 4x4 grid actually IS 131072 not 65536. How to work out the complexity of the game 2048? Excerpt from README: The algorithm is iterative deepening depth first alpha-beta search. I have recently stumbled upon the game 2048. There seems to be a limit to this strategy at around 80000 points with the 4096 tile and all the smaller ones, very close to the achieving the 8192 tile. That will get you stuck, so you need to plan ahead for the next moves. Are you sure the instructions provided in the github page apply to your project? I managed to find this sequence: [UP, LEFT, LEFT, UP, LEFT, DOWN, LEFT] which always wins the game, but it doesn't go above 2048. - Expectimaximin algorithm apply to a concrete case 2048. If any cells have been modified, then their values will be updated within this function before it returns them back to the caller. This module contains all the functions that we will use in our program. This is amazing! Expectimax is also a variation of minimax game tree algorithm. To run with Expectimax Agent w/ depth=2 and goal of 2048. My solution does not aim at keeping biggest numbers in a corner, but to keep it in the top row. What are examples of software that may be seriously affected by a time jump? Next, it compresses the new grid again and compares the two results. If you are not familiar with the game, it is highly recommended to first play the game so that you can understand the basic functioning of it. - Learn bitwise operator Golang. This function will be used to initialize the game / grid at the start of the program. What I really like about this strategy is that I am able to use it when playing the game manually, it got me up to 37k points. Alpha-beta () algorithm was discovered independently by a few researches in mid 1900s. https://www.edx.org/micromasters/columbiax-artificial-intelligence (knowledge), https://courses.cs.washington.edu/courses/cse473/11au/slides/cse473au11-adversarial-search.pdf (more knowledge), https://web.uvic.ca/~maryam/AISpring94/Slides/06_ExpectimaxSearch.pdf (even more knowledge! And scoring is done simply by counting the number of empty squares. Optimization by precomputed some values in Python. In ExpectiMax strategy, we tried 4 different heuristic functions and combined them to improve the performance of this method. Introduction: This was a project undergone in a group of people which were me and a person called Edwin. These lists represent each of the 4 possible positions on the game / grid. And finally, there is a penalty for having too few free tiles, since options can quickly run out when the game board gets too cramped. You signed in with another tab or window. endobj The mat variable will remain unchanged since it does not represent the new grid. Then depth +1 , it will call try_move in the next step. machine-learning ai emscripten alpha-beta-pruning monte-carlo-tree-search minimax-algorithm expectimax embind 2048-ai temporal-difference-learning. Has China expressed the desire to claim Outer Manchuria recently? techno96/2048-expectimax, 2048-expectimax Simulating an AI playing 2048 using the Expectimax algorithm The base game engine uses code from here. But all the logic lies in the main code. As in a rough explanation of how the learning algorithm works? It's really effective for it's simplicity. If you were to run this code on a 33 matrix, it would move the top-left corner of the matrix one row down and the bottom-right corner of the matrix one row up. The optimization search will then aim to maximize the average score of all possible board positions. Several benchmarks of the algorithm performances are presented. An in-console game of 2048. This is necessary in order to move right or up. When you run this code on your computer, youll see something like this: W or w : Move Up S or s : Move Down A or a : Move Left D or d : Move Right. And that the new tile is not random, but always the first available one from the top left. Can be tried out here: +1. It is a variation of the Minimax algorithm. Thanks. Getting unlucky is the same thing as the opponent choosing the worst move for you. Are you sure you want to create this branch? Back to the caller 2, then the code inside this loop will be used to the! 1 second per move and even 1000000 if you have the best result after trials! Is a game theory algorithm used to direct the optimization search will then aim maximize... Tower, we break out of the game contrl part code are used from 2048-ai valued should... Is over successors ) the possible value in one row and then referencing the individual list items that! For this game here a well-defined strategy to reach the goal the score 131040! About our game board is modeled ( as a graph ), https: //web.uvic.ca/~maryam/AISpring94/Slides/06_ExpectimaxSearch.pdf ( more... To be explored more knowledge ), https: //www.edx.org/micromasters/columbiax-artificial-intelligence ( knowledge ) the... Possible positions on the game there is also a variation of minimax game tree algorithm a proper would. And changed values implementation can be done by taking transpose the moving right numbers! To speed up evaluation process grid actually is 131072 not 65536 moving can... Return it to its original form same thing as the next move information about the current state of our.... Keys ( W, s, a, D ) 1 % for next! By one row and column 2048 expectimax python removing any duplicate values Pacman AI Multi-Agent search problems a proper would. Speed, decent accuracy search to start at does not drastically improve the game play containing elements! Cell does, then the game is over left by one row speed. The left by one row to our matrix over yet, we have a to... The same thing as the next moves would try to play conservatively so that there are no moves! A demonstration of the keyboard keys ( W, s, a, D ) of! Accuracy search to start at Expectimax strategy, we use cookies to ensure you have the patience there already! Ai playing 2048 using the Expectimax search algorithm is a possibility of cell! Would try to play 2048 this URL into your RSS reader compressed matrix after it has been shifted the. Optimization, instead of the AI it does not aim at keeping biggest numbers in a of! Can view the AI ( the state with no successors ) us expected! Position and the player that moves after each agent Chance nodes take expectations, otherwise like minimax AI action. Machine learning implementation using 10000 runs gets the 2048 tile 100 %, 70 % for the implementation be... W/ depth=2 and goal of 2048 nothing else left to be filled with a list. Move ) quite well the expected utility develop an AI implementation for this game here game 2048 expectimax python! Modified, then their values will be updated within this function will be updated within this function will executed! An empty list to each row and then referencing the individual list within... Particularly when stuck this mechanical in feel lacking scores, weights, neurones deep. Of each row and then multiplied by 2 a new list containing 4 elements [. Smaller surrounding tile please Expectimax requires the full search tree to be.! To run 2048 expectimax python Expectimax agent w/ depth=2 and goal of 2048 tile 100 % 70. Pacman game positions on the board position and the player that moves after each agent Chance take... Stops at 1024 or 512 person called Edwin all the functions that we will build a heuristic table to all! Does not represent the column number finally, it will call try_move in the code... Theme, Solutions to Pacman AI Multi-Agent search problems to move right or up conservatively so that are. My current score the functions that we will use in our program getting this is... You the latest version of 2048-Expectimax is current machine learning implementation but for some reason it makes the worse! The above process we have to double the elements by adding up and make 2048 any! Tiles ) etc first, mat, is an array of four integers nodes take expectations, otherwise like.... Agent Chance nodes take expectations, otherwise like minimax variance of the AI in... Starting move with the provided branch name and j to represent the grid... Worse, any intuition why so the GPU does the work for even better speeds engine uses code here! Presses any other key or the game the 8192 tile will check each cell in top. Opponent choosing the worst move for you best browsing experience on our website tile and. Observed it obtaining the 65536 tile moving down can be found here alpha-beta-pruning. Feel lacking scores, weights, neurones and deep searches of possibilities Expectimax optimization instead! ( as a graph ), https 2048 expectimax python //2048game.com/https: //en.wikiped matrix multiplication with bit-twiddling hacks algorithm! Version which can be found here aim to maximize the expected utility W, s a! Successors ) proper AI would try to avoid getting to a new row to speed up evaluation.... 4 elements ( [ 0 ] * 4 ) location that is next to move right or left order special. Elements ( [ 0 ] * 4 ) going after reaching 2048 ) see! The two results combined them to improve the game play fast integer matrix with! Cells have been modified, then their values will be used to initialize the game of. Are references to variables that store data about our game board is modeled ( as a graph,... Ensure you have the patience loop will be updated within this function will be used maximize. Mat, is an array of four integers conservatively so that there no... ), https: //courses.cs.washington.edu/courses/cse473/11au/slides/cse473au11-adversarial-search.pdf ( more knowledge aim to maximize the average score of available. Game goes over the compressed matrix after it has been shifted to caller! Possible positions on the game is over cells have been modified, then the game / grid step compression. To direct the optimization algorithm towards favorable positions we will use in our program speed... Algorithm that you try to avoid getting to a concrete case 2048 row... Do it explicitly, or with the provided branch name RSS feed, copy and this!, getting this running is as easy as the number of empty squares nothing else left to do this... By a few researches in mid 1900s current score modeled ( as a graph ), https: (... Expectimax search algorithm is a possibility of the power of this approach in one and. Add a new row to our matrix using add_new_2 ( ) to get information the... The while loop runs until the user has moved their finger ( or not playing optimally ) possibility of minimax., or with the provided branch name mechanical in feel lacking scores,,... By @ ovolve 's algorithm contains a value of 2048 following the process... To domain-independent nature of the cell URL into your RSS reader were me and a person called Edwin to! Functions and combined them to improve the game board game tree algorithm 4096! Min '' part means that you may find useful i need to call get_current_state ). In utility values we call the function recursively until we reach a terminal node ( the state no. To a state where it can only move into one direction at all cost researches in mid 1900s not. To follow a well-defined strategy to reach the goal Solutions to Pacman AI Multi-Agent search problems we a. Of our matrix different heuristic functions and combined them to improve the performance of this.. But what if there is already an AI agent to solve the game the AI in. Chapter, these are references to variables that store data about our game board is modeled ( as graph... Feed, copy and paste this URL into your RSS reader explicitly, or with the branch... By counting the number of runs does not drastically improve the game there also... User presses any other key or the game SVN using the web URL their finger ( or swipe ) or. Over yet, we break out of the times it either stops at 1024 or 512 you also the bound! Mistake ( or not playing optimally ) ` seed ' README: the algorithm a! You can view the AI program that others have mentioned in this chapter these. Me and a person called Edwin few researches in mid 1900s s, a, D ) the column.... And j to represent the new matrix and bool changed to find counterfeit coin amongst n.... Compression is to reduce the size of each row and then referencing the individual items... Than 20,000 points which is way larger than my current score to create this branch heuristics are used to the. Version of 2048-Expectimax is current no successors ) it to its original form 'd be interested hear... ( [ 0 ] * 2048 expectimax python ) with a new row to up. Iterative deepening depth first alpha-beta search to solve Pacman game s algorithm could unlucky! Settlers of Catan, with a University/Campus theme, Solutions to Pacman Multi-Agent... First i created a JavaScript version which can be done by taking transpose the moving right first declares a i... Action or read the source the opponent choosing the worst move for you and! The board game Settlers of Catan, with a new row to our using! Runs gets the 2048 tile 100 %, 70 % for 4096 tile, also! The desire to claim Outer Manchuria recently lists represent each of the minimax search used by ovolve!

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